Biostats test 2 Flashcards
deviation score
xi-x bar
sample variance
sum of all squared deviation scores divided by n-1. (s squared)
purpose of ANOVA
splitting total variance in two parts; one pertaining to differences between groups and one pertaining to differences within groups.
F
mean squares between groups (explained varianace; effect)/mean squares within groups (unexplained variance; error). if F takes on a sufficiently large value, we can reject H0 (still need to compare p versus alpha.
another definition of variance
total sum of squares divided by n-1
total sum of squares
basically the top half of variance; sum of squared deviation scores between all n data points (summed over all groups), relative to the grand mean (mean of all those n data points). between groups sum of squares + within groups sum of squares
within groups sum of squares
sum of squared deviation scores between each of k group’s individual values relative to that k group’s mean, summed over all groups
between groups sum of squares
sum of squared deviation scores between each between of k group means relative to grand mean
degrees of freedom
number of values that are free to vary given a boundary condition
how many degrees of freedom does variance have
n-1 because given a mean value, one degree of freedom is lost to compute the variance around the mean
df total sum of squares
n-1 because one mean is constrained by the others
df between groups sum of squares
k-1, one mean is constrained by the others
df within groups sum of squares
n-k (one degree of freedom is used up in calculating each groups mean, so since there are k groups ,we lost k degrees of freedom, one for each group mean)
mean squares
computed on basis of different sums of squares by dividing the sums of squares by their degrees of freedom; so mean squares for total squares is actually variance!
one way ANOVA
one factor, eg drug dose on mean reaction time
Assumptions for one way anova
within group variability is unexplained; considered error variance. we check for unequal precision using Levene’s
Levene’s test for homogeneity of error variance
H0: all of the group’s distribution and errors differ in approximately the same way, regardless of the mean for each group.
Factorial anova
two factors or more, can each have different levels. for example three drug dose levels and two biological sexes. 3x2 = 6 mean values. then we can also have interactions.
effect modification
effect of one IV on DV is different for levels of another IV
mushrooming
when adding factors to design multiplies effect modification terms
independent samples t-test
two independent groups, compare their means; like one way anova with just two levels
repeated measures t dest
matched, dependent samples t-test: comparison of paired values
one-sample t-test
on sample mean compared to a given, fixed value
MANOVA
multivariate analysis of variance - use when we wish to look at mean difference across several dependent variables because they are believed to be meaningfully related (eg multiple factors of a construct such as biodiversity, or health)
Hierarchy of when to use MANOVA and ANOVA
if we want to assess the effect of IVs on the collective body of DVs, we first use MANOVA. If there is no effect, we do not need to proceed. If there is an effect, we conduct ANOVA to find out for which DVs the IVs have an effect. For significant ANOVAs, we may want to compare the effect of factor levels.
When do we use repeated measures ANOVA
when we are comparing more than 2 means and the subjects are measured either at different time instants or in several conditions. time and condition are within-subject factors that create dependencies in the data.
difference between factors and levels
factor: drug dose. levels: low, medium, high
Repeated measures ANOVA -mixed
if both within-subject and between-subject factors are included in one model, eg comparing the effects of treatment type (BS, 2 levels) over 4 time (WS, 4 levels)
Sphericity assumption
difference scores between levels of a within-subjects factor have the same variance for the comparison of any two levels
Mauchly’s test
tests sphericity (equality of variance of difference scores between any two groups). If Mauchly’s W is significant, sphericity cannot be assumed. If sphericity assumptions is violated, df’s must be corrected (made smaller, more conservative) by some kind of scheme.
MANOVA for repeated measures
the sets of values measured at different time instants are considered different (but correlated) dependent variables. since we cannot look at difference scores when comparing scores on different variables, there is no more sphericity that could be violated.
What an interaction tells us in a two-way ANOVA (or repeated measures ANOVA with between-subjects factors)
an interaction effect occurs when the effect of one independent variable (treatment) on the dependent variable (CO2 uptake) is not consistent across the levels of another independent variable (population).
in cross-sectional studies on the elderly
investigator compares different age groups at the same moment in time on the variable
in longitudinal studies on the elderly
